The three techniques:

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• The three techniques

• Light scattering (LS)
• Small-angle x-ray scattering (SAXS)
• Small-angle neutron scattering (SANS)
• - Principles
• - Similarities and Differences
• - Advantages and disadvantages

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X-rays Light wavelength
Strong absorption
X-rays 0.05-0.15 nm
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What is in the courseAdvanced SuperStructures
Scattering Microscopy (ASSM)?
microworld
macroworld
X-rays
light
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Light scattering (LS)
Rayleigh scattering (point scatters ltlt ?)
Intensity is very weak and ? ?-4
Mie scattering on water droplets (comparable to /
larger than ?) Intensity is very strong for
all ?
These are beautiful but non-scientific examples!
Experiments are performed with a single ?
(monochromatic wave) To get quantitative data,
one needs careful index matching! (?n lt 0.1 at
least)
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Light scattering (LS)

• People usually talk about refractive index, not
  the scattering length density (scattering
  length density contrast is proportional to ?n).
• Not to be forgotten wavelength is a medium is
  different! ?medium ?0/n or k0 (2? / ?)n
• Also of importance Polarization effects

• Solution use a smart choice of polarization
  so that ? ?/2 (90o)

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X-rays from sealed tube
Cu anode
X-ray intensity
X-rays
V50kV
electrons
K?
K?
hot filament
0
M
L (2s and 2p)
?
K?
Energy levels in Cu atom
K?
K (1s)
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ESRF, Grenoble (France)
Synchrotron operatesat Ee 6 GeV
Ee ?mc2
mc2 0.5 MeV ? gt 104 v 0.999999996 c
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Source at BM-26 DUBBLEbending magnet
?-1 10-4 rad
(vertically)
Even broader fan horizontally
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Synchrotron radiation
Electron beam of energy E
Characteristic energy, Ec
E is in GeV , B is in T
Undulator
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Typical optical scheme of DUBBLE
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ESRF and Institut Laue Langevin
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Production of neutrons
de Broglie
Initial neutron energy ?1 MeV ? 0.0003 Å (not
useful!)
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ISIS Neutron Source
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Neutron Velocity selector
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ILL D22
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Neutron scattering lengths
Very bad
Very good
1 barn 10-28 m2
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Summary

• (static) LS
• Cheap, compact good for large-scale
• Too small K-range, multiple scattering,
  absorption
• Synchrotron SAXS
• Single scattering, large K-range, high
  brightness
• Expensive, low sensitivity to small atoms
• SANS
• Sensitivity to small atoms, large K-range,
  contrast variation
• Expensive, low intensity, incoherent background